% 附录与致谢
% 层级合作论文的所有附录部分

\appendix

\input{sections/appendices/appendix_a_spectral_proof}

\input{sections/appendices/appendix_b_master_equation}

\input{sections/appendices/appendix_c_info_thermo}

\input{sections/appendices/appendix_d_thermodynamics}

\input{sections/appendices/appendix_e_rg_universality}

\input{sections/appendices/acknowledgements}

